Small Perturbation Solutions for Parabolic Equations

2011/11/25 by Yu Wang, Wang, Yu · 5 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1111.5888

This is the version to appear in Indiana Univ. Math. J. We have corrected few typos and errors that occur in earlier versions. We have also rewritten the statement of Lem.2.2 and detailed the proof of Lem 2.2-2.4

openalex publication_date 2011/11/25 · arxiv created 2012/05/31 · arxiv updated 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ϕ be a smooth solution of the parabolic equation F(D²u, Du, u, x, t)- u_t = 0: Assume F is uniform elliptic only in a neighborhood of (D²ϕ, Dϕ, ϕ, x, t), we prove that any solution obtained from small L1-perturbation of ϕ remains smooth.

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